In Texas
Hold'em, each player receives two "hole" cards face down, and
five face up community cards are dealt in the center of the table. The
player who makes the best five-card poker hand with any combination of
their two hole cards and the five community cards wins the round.

In a Texas
Hold'em game, a disc or other marker is used to indicate which person
is the "dealer" for the round. Before the cards are dealt, the
two players to the left of the dealer post forced bets called blinds.
The person immediately to the left of the dealer posts a bet called the
small blind, which is usually equal to half of the minimum bet. The person
to the left of the small blind posts the big blind, which is equal to
the minimum bet. The first two cards are dealt to each player face down
(these are called the hole cards), and the person to the left of the big
blind starts the first round of betting. (Notice that the big blind and
small blind do not get to look at their cards before betting, thus the
term "blind").

In the first
round of betting, each player has three options: call, raise or fold.
To call, the player must place a bet that is equal to the last bet placed.
(For the first player in the round, this would be equal to the minimum
bet.) A player may choose to raise their bet by an additional amount,
which the other players will then have to call. If one's hole cards are
not favorable, the player may simply choose to fold and sit out the round.

After all
the players have finished the first round of betting, the first three
community cards are dealt face up on the board. This is called the flop.
The second and all subsequent betting rounds start with the first player
to the dealer's left, and players now has the option to check. By checking,
the player indicates interest in the pot without placing a bet. Any player
may choose to place a bet, which the other players must then call. Players
can still raise, if a bet has been made, or fold, if their hand is not
favorable.

After the
second betting round, the fourth community card is dealt face-up (this
is called the turn card). In limit games, the minimum bet doubles in the
last two rounds of betting. After the third betting round, the fifth and
final community card is dealt (this is called the river card). A final
round of betting ensues, and afterwards each player turns their hole cards
face up in the order that they bet. The highest hand that can be made
with any combination of a player's hole cards and the five community cards
wins the pot. If two or more players have the same hand, the next highest
card in the player's hand (the kicker) is used to break a tie. If there
is no kicker card (the tied players have used both hole cards, or have
the exact same five card hand), then the pot is split between them. The
dealer button is then passed clockwise to the next player and another
round of play begins.

Poker Platoon
has a clear graphical summary of the rules of Texas Hold'em

There are
three kinds of Hold'em games. In Limit games, bets and raises are set
at a fixed amount. A typical limit game would be $10/$20 ($10 minimum
bet for the first two rounds, and $20 minimum for the last two rounds.)
The big blind would be equal to the minimum bet ($10) and the small blind
would be half the minimum bet ($5). Each round of betting is capped at
a maximum number of raises, depending on the rules of the game. In online
Hold'em games, raises are generally capped at four bets per round. New
players will start with low-limit games and gradually work their way up
to higher limits as their skill progresses.

In No Limit
Hold'em, the maximum bet is determined by the number of chips you have
in front of you. Players can bet and raise by any amount, and at any time,
a player can go "all-in" by pushing all their chips toward the
center of the table. To call, the other players at the table must push
in all of their chips, up to the amount of their opponent's all-in bet.
This is the type of Hold'em that is played on the pro level, and on TV
shows such as the World Poker Tour and the World Series of Poker.

Pot Limit
Hold'em is similar to No Limit, except that the maximum bet is determined
by the number of chips currently in the pot. This allows players to experience
the excitement and strategy of No Limit Hold'em without the necessity
of a large bankroll. Pot Limit games usually have a maximum buy-in (the
number of chips you start with) to keep the game competitive.